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Show that f'(a) = g(a) ?

  1. May 6, 2012 #1
    1. The problem statement, all variables and given/known data

    Problem:
    1C-2 Let f(x) = (x - a)g(x). Use the definition of the derivative to calculate that f'(a) = g(a), assuming that g is continuous



    2. Relevant equations



    3. The attempt at a solution

    I just started a self study of calculus using Khan and MIT OpenCourse. I am bit stuck, or maybe confused, with this exercise from MIT 18.01

    The definition for the derivative is
    [itex]\frac{Δy}{Δx}[/itex]=[itex]\frac{f(x)-f(a)}{x-a}[/itex]

    I can replace f(x) with (x-a)g(x), but I don't know what to do with f(a). In the given solution f(a) somehow becomes 0, but I can't see how.

    The given solution:
    attachment.php?attachmentid=47038&stc=1&d=1336362033.png

    Any help is much appreciated.
     

    Attached Files:

  2. jcsd
  3. May 6, 2012 #2

    LCKurtz

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    f(a) = (a-a)g(a) = 0.
     
  4. May 7, 2012 #3
    ah - of course. Thank you very much
     
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